This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A261821 #8 Sep 29 2015 12:31:33
%S A261821 4,11411,1114111,18111411181,741811141118147,1674181114111814761,
%T A261821 90167418111411181476109,3901674181114111814761093,
%U A261821 14390167418111411181476109341,9143901674181114111814761093419,75914390167418111411181476109341957
%N A261821 Minimal nested palindromic primes with seed 4.
%C A261821 Let s be a palindrome and put a(1) = s. Let a(2) be the least palindromic prime having s in the middle; for n > 2, let a(n) be the least palindromic prime have a(n-1) in the middle. Then (a(n)) is the sequence of minimal nested palindromic primes with seed s.
%H A261821 Clark Kimberling, <a href="/A261821/b261821.txt">Table of n, a(n) for n = 1..200</a>
%e A261821 As a triangle:
%e A261821 .........4
%e A261821 .......11411
%e A261821 ......1114111
%e A261821 ....18111411181
%e A261821 ..741811141118147
%e A261821 1674181114111814761
%t A261821 s = {4}; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#]]]] &]; AppendTo[s, tmp], {15}]; s
%t A261821 (* _Peter J. C. Moses_, Sep 01 2015 *)
%Y A261821 Cf. A261881 (seed 0, with guide to related sequences).
%K A261821 nonn,easy,base
%O A261821 1,1
%A A261821 _Clark Kimberling_, Sep 23 2015